Answers
Look at the picture.
ΔABC and ΔDAC are similar. Therefore the sides of the triangles are in proportion:
[tex]\dfrac{AC}{BC}=\dfrac{DC}{AC}[/tex]
AC = x
BC = 5 + 4 = 9
DC = 4
Substitute:
[tex]\dfrac{x}{9}=\dfrac{4}{x}[/tex] cross multiply
[tex]x^2=(9)(4)\\\\x^2=36\to x=\sqrt{36}\\\\\boxed{x=6\to C)}[/tex]
Related Questions
Stu takes a job with a starting salary of $65,000 for the first year. He earns a 2% increase each year. How much does Stu make over five years?
$325,000
$331,500
$338,263
$358,826
Answers
Answer:
Stu makes $338,263 over five years.
Step-by-step explanation:
In order to find the total amount Stu would make after five years, you need to find out how much he will make each year based on the 2% increase. Starting with year 1 at $65,000, we need to take his total salary and multiply by 1.02 (or the whole salary plus an increase of 2%). So, in year 2, he would make $66,300. Again, we would take his year 2 total salary and multiply by 1.02 to get $67,626 for year 3. We apply these same steps to years four ($68,978.52) and five ($70,358.10). To find his income over the five years, we need to add his salary from all five years together to get a total of $338,263.
Answer:
Option C which is $ 338,263
Step-by-step explanation:
The salary for the first year = $65,000
Increase per year= 2 %
To find total money made in five years = ?
total earned in first year = $65,000
Total increase in money after first year = 2 % of 65,000
= [tex]\frac{2*65000}{100}[/tex]
=$ 1300
Total earned in second year = 65,000 + 1300
= $ 66,300
Total increase in money after second year = 2 % of 66,300
= [tex]\frac{2*66300}{100}[/tex]
=$ 1326
Total earned in third year = 66300 + 1326
= $ 67,626
Total increase in money after third year = 2 % of 67,626
= [tex]\frac{2*67626}{100}[/tex]
=$ 1352.52
Total earned in fourth year = 67626 + 1352.52
= $ 68978.52
Total increase in money after fourth year = 2 % of 68978.52
= [tex]\frac{2*68978.52}{100}[/tex]
=$ 1379.58
Total earned in fifth year = 68978.52 + 1379.58
= $ 70358.1
Total Made in all five years = 65000+66300+67626+68978.52+70358.1
= $ 338262.62
≅$ 338,263
Find the length of the hypotenuse
Answers
We know that : In a Triangle, If Two Angles are Equal then Corresponding Sides with Respect to those Two Angles Should be Equal.
In the Given Right Angled Triangle, There are Two Angles which are Equal to 45°. It means The Lengths of the Sides Corresponding to those Equal 45° Angles should be Equal.
It Means The Given Right Angled Triangle is also an Isosceles Triangle
⇒ The Other Side of the Triangle is [tex]3\sqrt{2}[/tex]
As it is a Right Angled Triangle :
[tex]\mathsf{\implies (Hypotenuse)^2 = (3\sqrt{2})^2 + (3\sqrt{2})^2}[/tex]
[tex]\mathsf{\implies (Hypotenuse)^2 = 18 + 18}[/tex]
[tex]\mathsf{\implies (Hypotenuse)^2 = 36}[/tex]
[tex]\mathsf{\implies (Hypotenuse) = 6}[/tex]
The Length of Hypotenuse is 6
A line contains the points S (4, -10) and B (10, -16). Find the slope of ̅̅̅̅SB. Must show your work to receive full credit.
Answers
Answer:
The slope is -1
Step-by-step explanation:
To find the slope when we have 2 points, we can use the formula
m = (y2-y1)/(x2-x1)
= (-16--10)/(10-4)
= (-16+10)/(10-4)
= -6/6
= -1
The slope is -1
Find the measure of 1
A. 104
B.38
C.76
Answers
Answer:
a
Step-by-step explanation:
104 is the only number inside the box
The value of ∠1 is 38 degree , Option B is the correct answer.
What is a Parallelogram ?Parallelogram is a polygon with four sides , Opposite sides are parallel and equal.
From the figure given
One of the angle is 104 degree
when two lines are parallel and intersected by a transversal
then the sum of the consecutive interior angles is 180 degree
∠1 + ∠2 = 180 -104 = 76 degree
similarly the other two lines are parallel with each other
so ∠1 = ∠4
∠3 = ∠2
Therefore the diagonals are bisecting the angle and so
the value of ∠1 = 76 / 2 = 38 degree
Therefore , The value of ∠1 is 38 degree , Option B is the correct answer.
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Dean has 6 2/5 cups of yogurt. If it takes 4/5 cup of yogurt to make a fruit smoothie, how many smoothies can he make?
Answers
Answer:
8
Step-by-step explanation:
Change mixed number to decimal 6 2/5 = 6.4
Change needed fraction to decimal 4/5 = 0.8
Divide yogurt by yogurt needed 6.4 / 0.8 = 8
Working the problem like this will help you with any same type of problem.
If this helped a Brainliest ,Rating ,and/or a thanks will be appreciated
Answer: He can make 8 smoothies.
Step-by-step explanation:
Given : The total amount of yogurt Dean has = [tex]6\dfrac{2}{5}[/tex] cups
In Improper fraction , it will be :
[tex]6\dfrac{2}{5}=\dfrac{6\times5+2}{5}=\dfrac{32}{5}[/tex]
Also, the amount of yogurt required for a fruit smoothie = [tex]\dfrac{4}{5}[/tex]
Now , The number of smoothies he can make = (Total amount of yogurt Dean has) ÷ (amount of yogurt required for a fruit smoothie )
[tex]=\dfrac{32}{5}\div\dfrac{4}{5}\\\\=\dfrac{32}{5}\times\dfrac{5}{4}=8[/tex]
Hence, he can make 8 smoothies.
Lm is the midsegment of trapezoid ABCD ab=46 dc=125 what is lm
A. 103.5
B. 63
C. 79
D. 85.5
Answers
Answer: Choice D) 85.5
Work Shown:
To get the midsegment, we add up the sides parallel to this midsegment, then we divide by 2.
LM = (AB + DC)/2
LM = (46 + 125)/2
LM = 171/2
LM = 85.5
Answer: D is the answerb
a soccer team hopes to win at least 3 games for every 2 lost during the season. if there are 15 games scheduled, how many games can the team lose and still achieve its goal
Answers
Answer:
This team can lose 6 games and still achieve this goal.
Step-by-step explanation:
In order to find this, we can create a proportion and solve by cross multiplying. The proportion should compare amount of losses to total games.
Ratio = Total
2/5 = x/15
Now cross multiply
15*2 = 5x
30 = 5x
6 = x
This means the team can lose 6 games and still keep the necessary ratio.
What is the value of a
A. 27.5
B. 45
C. 50
D. 90
Answers
Answer:
90 degrees
Step-by-step explanation:
The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12 h more than the airplane. Determine the average speeds of the train and the airplane.
Answers
Answer
Average speed of the train = 90 km/h and average speed of the airplane = 360 km/h.
Explanation:-
If speed of train = x then the speed of airplane = 4x km/h and we have the 2 equations
x = 1440 / (t + 12) (t = time taken by the train)
4x = 1440 / t................................(1) (t = time taken by train)
Multiply the first equation by 4:-
4x = 5760 / (t + 12).....................(2)
Combining equations (1) and (2):-
1440 / t = 5760 / (t + 12)
Cross multiplying:-
5760t = 1440t + 17,280
4320t = 17,280
t = 17280/4320
t = 4 hours
speed of train = 1440/ (4 + 12) = 90 km/h and speed of plane = 4*90 = 360 km/h.
if f(x)=5x-7 then f^-1=__ _
Answers
Answer:
f^-1(x) = (x +7)/5
Step-by-step explanation:
Set x = f(y) and solve for y.
... x = 5y -7
... x+7 = 5y
... (x+7)/5 = y . . . . this is the inverse function
f^-1(x) = (x +7)/5
Mallory has 535 e-mail messages in her inbox. She sorts them evenly among folders labeld family,work, school and recipes.How many messages does mallory put in each folder
Answers
Anwser could be 107 because 535/5=107
which of the following are roots of the polynomial function below? F(x)=x^3-3x^2+2
Answers
The roots of the polynomial function F(x)=x^3-3x^2+2 can be found by reducing the function to zero and solving for x, likely by applying synthetic division or the Rational Root Theorem, as the polynomial is of third order.
Explanation:In Mathematics, especially in algebra, we often encounter the concept of finding the roots of polynomial functions. The roots of the function F(x)=x^3-3x^2+2 can be found by setting the function equal to zero and solving for the variable x:
Step 1: Set the equation to zero: x^3-3x^2+2 = 0.Step 2: Try to factor the polynomial or use a solving method such as the quadratic formula if it was a second-order polynomial. But in this case, the polynomial is of third order, and in such cases you typically apply synthetic division or the Rational Root Theorem to find the roots.Note: This explanation suggests general approaches. The actual solution would require longer calculations.
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The only root of the polynomial function F(x) = x³ - 3x² + x + 5 is 2 + i.
Explanation:Let's go through the possible roots of this polynomial function one by one and see which of them will make the function equal to zero. Recall that if a number p is a root of a polynomial, then when we substitute p into the polynomial, the resulting value will be zero.
A. First, let's consider 2+i as a possible root.
We would evaluate F(2+i) = (2+i)³ - 3(2+i)² +(2+i) + 5 = 0.
Upon evaluation, it turns out that F(2+i) does indeed equal 0.
B. Now let's see if -2+i is a root.
We evaluate F(-2+i) = ((-2+i)³ - 3(-2+i)² + (-2+i) + 5. This happens not to equal 0. Therefore, -2+i is not a root.
C. Then, we check if 1 is a root by computing
F(1) = 1³ - 3×1² +1 +5. Upon computing, we find that this doesn't result in 0 either. So, 1 is not a root
D. Finally, let's check if 2 is a root.
We compute F(2)= 2³ - 3×2² +2 +5. This computation also doesn't result in 0, therefore 2 is not a root of the polynomial function.
In conclusion, the only given number that is a root of the function is 2 + i.
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Question:Which of the following are roots of the polynomial function below?
F(x)=x³-3x²+x+5
A. 2+i
B. -2+i
C. 1
D. 2
A seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus. How many yards will she need to make costumes for all 25 students in chorus?
Answers
Answer:
100 yards
Step-by-step explanation:
It takes 4 yards of fabric to make a costume for one student. She needs to make costumes for every student in chorus, so you just multiply this number by 25 and get 100 yards.
Answer:
100 yards.
Step-by-step explanation:
We have been given that a seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus.
We will use proportions to solve the given problem.
[tex]\frac{\text{Yards of fabric}}{\text{Costumes}}=\frac{12}{3}[/tex]
[tex]\frac{\text{Yards of fabric}}{25}=\frac{12}{3}[/tex]
[tex]\frac{\text{Yards of fabric}}{25}*25=\frac{12}{3}*25[/tex]
[tex]\text{Yards of fabric}=4*25[/tex]
[tex]\text{Yards of fabric}=100[/tex]
Therefore, 100 yards of fabric is needed to make costumes for 25 students.
Each group member is permitted to consume one-third of a pizza. If there are twenty-four members in the group, how many pizzas should be ordered?
Answers
Answer:
8
Step-by-step explanation:
so they are one third of a pizza so thats 1/3 and 24 memebers so basically you just have to multiply 1/3 x 24 = 24/3 which is 8.
Answer:
8 pizzas should be ordered.
Step-by-step explanation:
To get the number of pizzas to be ordered, all we simple need to do is to multiply the numbers of the group members by the amount to be consume by each group member. That is;
Number of pizzas to be ordered = amount to be consume by each group member × number of group members.
amount to be consume by each group member = [tex]\frac{1}{3}[/tex]
Number of group members = 24
We can now proceed to insert our values into the formula
Number of pizzas to be ordered = amount to be consume by each group member × number of group members.
Number of pizzas to be ordered = [tex]\frac{1}{3}[/tex] × 24
= [tex]\frac{24}{3}[/tex]
= 8
Number of pizzas to be ordered = 8
Therefore, 8 pizzas should be ordered.
This table shows the input and output values for an exponential function f(x) .
What is the ratio of outputs for any two inputs that are three values apart?
x −3 −2 −1 0 1 2 3
f(x) 8/27 8/9 8/3 8 24 72 216
Enter your answer, as a simplified fraction
Answers
Answer:
Given the table as shown below:
x y
-3 8/27
-2 8/9
-1 8/3
0 8
1 24
2 72
3 216
Taking any input variable x that are three apart:
i,e x = 0 and x = 3
The output values at x =0 and x = 3 are:
f(0) = 8 and f(3) = 216
Then;
The ratio of outputs is:
[tex]\frac{f(3)}{f(0)} = \frac{216}{8}= \frac{27}{1}[/tex] or 27 : 1
Therefore, the ratio outputs for any two inputs that are three values apart is: [tex]27: 1[/tex]
Answer:
0.5
Step-by-step explanation:
A manufacturer of shipping boxes has a box shaped like a cube. The side length is (5a + 4b). What is the volume of the box in terms of A and b
Answers
The volume of the cube would be S^3, where S is the length of the side.
Volume = (5a + 4b)^3
Which becomes:
(5a+4b)(5a+4b)(5a+4b)
Multiply the first two sets of parenthesis by each other:
(25a^2+40ab+16b^2)(5a+4b)
Now multiply that by the 3rd set of parenthesis to get:
125a^3+300a^2b + 240ab^2 + b^3
Which value must be added to the expression x^2+16 to make it a perfect square trinomial
Answers
Adding the term 8x we will get:
x² + 8x + 4² = (x + 4)²
How to make a perfect square trinomial?
The perfect square trinomial is:
(a + b)² = a² + 2ab + b²
Here we start with:
x² + 16
We can rewrite this as:
x² + 4²
We can see that the term missing is the cross one, which will be:
2*(x)*4 = 8x
Then we will get:
x² + 8x + 4² = (x + 4)²
Beth and Carley are selling candy bars to raise money for new cheerleading uniforms. Beth has sold one less than twice the number of candy bars that Carley has sold. If they have sold 188 candy bars in all, how many has Beth sold?
Answers
Answer:
125 candy bars
Step-by-step explanation:
[tex]\text{Let the number of candy bars sold by Carley is }x\\\text{Then since Beth has sold one less than twice the number of candy bars}\\\text{that Carley has sold, so number of candy bars sold by Beth}=2x-1\\\\\text{also given that they have sold 188 candy bars in all, so we have}\\\\\text{Candy bars sold by Carley + Candy bars sold by Beth}=188\\\\\Rightarrow (x)+(2x-1)=188\\\\\Rightarrow 3x-1=188\\\\\Rightarrow 3x=189\\\\\Rightarrow x=\frac{189}{3}=63[/tex]
[tex]\text{Hence the candy bars sold by Beth are:}\\=2x-1\\\\=2(63)-1\\\\=126-1\\\\=125\\\\\text{Hence, Beth sold 125 candy bars.}[/tex]
Anumeha is mowing the lawns for a summer job. For every mowing job, she charges and initial fee of $10 plus a constant fee for each hour of work. Her fee for a 5-hour job, for instance is $35. Let F(t) denote Anumeha's for a single job F (measured in dollars) as a function of the number of hours t it took her to complete it. Write the functions formula
Answers
Answer:
F(t) = 10 +5t
Step-by-step explanation:
Income equals the initial fee plus the hours worked times the hourly rate
We know the initial fee = 10
hours = t
hourly rate =r
F(t) = 10 + r*t
We know a 5 hour job is 35 dollars
35 = 10 + r*5
Subtract 10 from each side
35-10 = 10-10 +5r
25 = 5r
Divide by 5
25/5 = 5r/5
5 =r
The hourly rate is 5
F(t) = 10 +5t
Montel sold 13 popcorn buckets and sold 13 fruit baskets for a fundraiser. The fruit baskets coast $20.75 each . If Montel raised a total of $469, how much did each popcorn buckets coast
Answers
Answer:
The popcorn buckets each cost around $15.34.
Step-by-step explanation:
how can we write 128 in exponent form?
Answers
[tex] log_{n }(128) [/tex]
Answer: 2⁷
Step-by-step explanation:
128
∧ 2 64 ∧ 2 32 ∧ 2 16 ∧ 2 8 ∧ 2 4 ∧ 2 2128 = 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2⁷
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.)
midpoint (-18,-12) endpoint (-9,-11)
Answers
[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\text{We have}\\\\\text{endpoint}\ (-9,\ -11)\to x_1=-9,\ y_1=-11\\\\\text{midpoint}\ (-18,\ -12)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-9+x_2}{2}=-18\qquad\text{multiply both sides by 2}\\\\-9+x_2=-36\qquad\text{add 9 to both sides}\\\\\boxed{x_2=-27}\\\\\dfrac{-11+y_2}{2}=-12\qquad\text{multiply both sides by 2}\\\\-11+y_2=-24\qquad\text{add 11 to both sides}\\\\\boxed{y_2=-13}\\\\Answer:\ \boxed{(-27,\ -13)}[/tex]
A polynomial function has a root of zero with multiplicity one, and root of two with multiplicity four. If the function has a negative leading coefficient, and is of odd degree, which of the following is true.
- the function is positive on (-infinity, 0)
-the function is negative on (0,2)
-the function is negative on (2,infinity)
-the function is positive on (0, infinity)
Answers
Answer: A, B, and C
Step-by-step explanation:
root of zero (x = 0) with multiplicity of 1 (x = 0)¹ means that the graph CROSSES the axis at x = 0
root of two (x = 2) with multiplicity of 4 (x = 2)⁴ means that the graph TOUCHES the axis at x = 2
WHY?
odd numbered multiplicity crosses the x-axiseven numbered multiplicity touches the x-axis (it is a turning point)Leading Coefficient (end behavior of right side):
If the leading coefficient is positive, then right side goes to +∞If the leading coefficient is negative, then right side goes to -∞Degree of polynomial (left side behavior):
If degree is even, then left side is the same as the right sideIf the degree is odd, then left side is opposite of right sideThe given polynomial has a negative leading coefficent and odd degree so the left side goes to +∞ and the right side goes to -∞
OBSERVE INTERVALS:
(-∞, 0) is above the x-axis so POSITIVE(0, 2) is below the x-axis so NEGATIVE(2, +∞) is also below the x-axis x=2 was a turning point so NEGATIVESee graph to confirm statements above
Answer:
A, B, and C
Step-by-step explanation:
Had the same question on Edge :)
PLEASE ANSWER THIS QUESTION TOO !! FOR 30 POINTS AND BRAINLIEST!!
Answers
Answer:
3000 books
Step-by-step explanation:
We know the author receives a one time fee of $2500. On top of that, the author will receive $1.50 per book sold. This is a constant rate and is linear because of this. We can use y=mx+b. M is the slope or rate of change. M here is $1.50. B is the starting value which is $2500 here.
We write y=1.5x+2500.
This equation will give the amount of money the author earns for x number of books sold. If y=7000 for the author earning 7000. We will use inverse operations to isolate and find x.
7000=1.5x+2500
7000-2500=1.5x+2500-2500
4500=1.5x
4500/1.5=x
3000=x
Answer:
The author must sell 300 books.
Step-by-step explanation:
The total amount earned = advance + books sold * money per book
We know they want to make 7000
The advance is 2500
They earn 1.50 for each book sold
b= number of books sold
Substituting in
7000= 2500 + 1.5b
Subtract 2500 from each side
7000-2500 = 2500-2500 + 1.5 b
4500 = 1.5 b
Divide each side by 1.5
4500/1.5 = 1.5b/1.5
3000 = b
Identify a pattern and sequence and fine the next number in the pattern. 54,52,26,24,_,_,_
Answers
Answer:
54, 52, 26, 24, 22, -6, -4
Step-by-step explanation:
The hospital shop buys cereal bars in packs of 4. In one day they sell 58 cereal bars. How many packets did they open tht day?
Answers
You conduct an experiment where you roll a die and record the results. You roll the die 1,230 times, and the results are shown in the table below:
Result Frequency
1 245
2 172
3 219
4 201
5 137
6 256
What is the experimental probability of rolling a 1 on your next roll?
A.
0.1667
B.
0.1992
C.
0.245
D.
0.3275
Part B. What is the theoretical probability of rolling a 3 on your next roll?
A.
0.167
B.
0.178
C.
0.245
D.
0.333
The probability of an event is
2/7
What are the odds of the same event?
A. 7/9
B. 5/7
C. 2/9
D. 2/5
If I could get some help That'd Be Greattt
Answers
Answer: Other guy is right for 1 & 2 but is wrong for the last question.
I got a 100 on connections.
(1) 0.1992
(2)0.167
(3) 2/5
Step-by-step explanation:
The experimental probability of rolling a 1 on the next roll is 0.1992 (B). The theoretical probability of rolling a 3 on a six-sided die is 0.1667 (A). The odds of an event with a probability of 2/7 are 2 to 5 (D).
Explanation:The experimental probability of rolling a 1 in this experiment is calculated by dividing the frequency of rolling a 1 by the total number of rolls. There were 245 occurrences of rolling a 1 out of 1230 total rolls. To find the experimental probability, you divide 245 by 1230, which gives you 0.1992.
Part B: The theoretical probability of rolling any particular number on a fair six-sided die is 1/6, because there are 6 possible outcomes and each outcome is equally likely if the die is fair. Therefore, the theoretical probability of rolling a 3 on the next roll is 0.1667 (which is equivalent to 1/6 when rounded to four decimal places).
When the probability of an event is 2/7, the odds of the event are 2 to 5 (not 2/5). This is because odds are expressed as the ratio of the number of successful outcomes to the number of unsuccessful outcomes. Since there are 2 chances of success and 5 chances of failure (7-2=5), the odds are 2 to 5.
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Eva and Emily can clean the entire house in 4 hours. Eva can do it by herself in 6 hours. How long would it take Emily to do it by herself?
Answers
Answer:
12 hours would take emily
Step-by-step explanation:
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What expression can be used to determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds of flour for $0.74 per pound?
Answers
The expression for determining the total cost of buying granola and flour is (3.25/g) * g + (0.74/f) * f. The values of g and f represent the number of pounds of each item. To find the total cost, substitute the values into the expression.
Explanation:The expression that can be used to determine the total cost is:
Total cost = ($3.25/g) * g + ($0.74/f) * f
where 'g' represents the number of pounds of granola and 'f' represents the number of pounds of flour.
For example, if you wanted to find the total cost of buying 5 pounds of granola and 2 pounds of flour, you would substitute g = 5 and f = 2 into the expression to get:
Total cost = ($3.25/5) * 5 + ($0.74/2) * 2 = $16.25 + $1.48 = $17.73
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The total cost of buying g pounds of granola at $3.25 per pound and f pounds of flour at $0.74 per pound can be determined using the expression 3.25g + 0.74f.
To determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds of flour for $0.74 per pound, you can use the following expression:
3.25g + 0.74f
Here's a step-by-step explanation:
For granola, the cost per pound is $3.25. Therefore, for g pounds, the total cost is 3.25g.For flour, the cost per pound is $0.74. Therefore, for f pounds, the total cost is 0.74f.Add the costs together to get the total cost: 3.25g + 0.74f.This expression gives you the total cost based on the quantities of granola and flour you wish to purchase.
A rectangular garden is 17 feet wide. Its length is 3 feet more than twice the width. What is the area of the garden?
Answers
Answer:
a = 629
Step-by-step explanation:
a = w * L
w = 17
L = 2w + 3
a = (17) * (2w + 3)
a = (17) * (2(17) + 3)
a = 17 * (34 + 3)
a = 17 * (37)
a = 629